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Generalized Musical Intervals and Transformations$
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David Lewin

Print publication date: 2007

Print ISBN-13: 9780195317138

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780195317138.001.0001

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Generalized Interval Systems (3): A Non-Commutative GIS; Some Timbral GIS Models

Generalized Interval Systems (3): A Non-Commutative GIS; Some Timbral GIS Models

Chapter:
(p.60) 4 Generalized Interval Systems (3): A Non-Commutative GIS; Some Timbral GIS Models
Source:
Generalized Musical Intervals and Transformations
Author(s):

David Lewin

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195317138.003.0004

This chapter explores one non-commutative Generalized Interval System (GIS) of musical interest: the elements of the system are formal time-spans. It presents an extended discussion of a passage from Carter’s First Quartet which demonstrates the pertinence of this GIS to exploring music in which there are functional measured relations among time spans, but no one overriding time span that acts as a unit to measure all others. The chapter presents two examples of timbral GISs, and ends with a methodological note on the relations of music theory, perception, and the intuitions of a listener. Some motivic work by Chopin is considered in this connection.

Keywords:   Generalized Interval System, times spans, Carter, First Quartet, music theory, Chopin

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